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ashok kumar Grade: 11
        find the integral solutions of the equation (1-i)^x=(2)^x
6 years ago

Answers : (4)

Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
										

Dear Student,


Taking Log on both sides,u get xlog1/logi = xlog2


U have log1=0 and log2 is not equal to 0,which means x has o be zero


and that is the only integral solution


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6 years ago
Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
										

Dear Student,


Sorry for the wrong reply,i went wrong somewhere...


Anyways,taking Log on both sides,u get xLog(1-i) = x Log2


multiply and divide 1-i by root 2,u get 1-i/2^0.5 = e^-ipie/4


that is x( 0.5Log2 - i22/28 ) = xLog2


that is xLog2 = -i22/28 and x=0 are the solutions


clearly,x is imaginary if the 1st eqn is true,hence,x=0 is the only integral solution


 


THANKS


ALL THE BEST


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6 years ago
mycroft holmes
271 Points
										

6 years ago
Vishva vivek singh
13 Points
										(1-i)^x=2^x1-iComplex number is of the from x+iyWhere x=1             Y=-1I 1-i l=√x^2+y^2l 1-i l=√2 Hence  l 1-i l^x=2^x  Putting value     (√2)^x=2^x     √2^x=(√2×√2)^x    √2^x=(√2)^2x  Comparing powers           x=2x           x-2x=0            -x=0              X=0
										
2 months ago
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